As I recall, Teddy Seidenfeld is a fan of finite additivity.
Do you know why?
The recent thread on optional stopping and Bayes led me to this paper, which I see Seidenfeld is one of the authors of, which argues that countable additivity has bad consequences. But these consequences are a result of improper handling of limits, as Jaynes sets forth in his chapter 15. Seidenfeld and his coauthors go to great lengths (also here) exploring the negative consequences of finite additivity for Bayesian reasoning. They see this as a problem for Bayesian reasoning rather than for finite additivity. But I have not seen their motivation.
If you’re going to do probability on infinite spaces at all, finite additivity just seems to me to be an obviously wrong concept.
ETA: Here’s another paper by Seidenfeld, whose title does rather suggest that it is going to argue against finite additivity, but whose closing words decline to resolve the matter.
Do you know why?
The recent thread on optional stopping and Bayes led me to this paper, which I see Seidenfeld is one of the authors of, which argues that countable additivity has bad consequences. But these consequences are a result of improper handling of limits, as Jaynes sets forth in his chapter 15. Seidenfeld and his coauthors go to great lengths (also here) exploring the negative consequences of finite additivity for Bayesian reasoning. They see this as a problem for Bayesian reasoning rather than for finite additivity. But I have not seen their motivation.
If you’re going to do probability on infinite spaces at all, finite additivity just seems to me to be an obviously wrong concept.
ETA: Here’s another paper by Seidenfeld, whose title does rather suggest that it is going to argue against finite additivity, but whose closing words decline to resolve the matter.